Summary

The diagram below shows the information obtained from a set of 4 probes. As explained
in our first observation, the convex hull of the contact points defines
the inside region (black). The second observation allows us to discard
many points that cannot belong to the shape due to conflicts with the probe
paths (white). The remaining points (gray) are in the maybe set:
not enough information is available to classify them. The subsequent probes
will be aimed to reduced the size of the gray regions.

Note that the shape of the gray regions varies. The top region forms a
triangle. This property will be used later on to optimally aim probes.
The regions on the right and at the bottom widen away from the shape and the bottom shape is actually infinite. The region on the left also
forms a triangle but notice that, unlike the top region, one of the sides is bounded by a
probe path.

The next figure illustrates one possible shape. As you can see, the shape fits
exclusively in the maybe and inside regions. The inside
set is entirely part of the shape. Any shape with these properties is
a plausible candidate.